Virus Spread in Networks

The influence of the network characteristics on the virus spread is analyzed in a new-theN-intertwined Markov chain-model, whose only approximation lies in the application of mean field theory. The mean field approximation is quantified in detail. TheN-intertwined model has been compared with the exact 2N-state Markov model and with previously proposed ldquohomogeneousrdquo or ldquolocalrdquo models. The sharp epidemic threshold tauc, which is a consequence of mean field theory, is rigorously shown to be equal to tauc= 1/(lambdamax(A)) , where lambdamax(A) is the largest eigenvalue-the spectral radius-of the adjacency matrixA. A continued fraction expansion of the steady-state infection probability at nodejis presented as well as several upper bounds.